Model selection using multivariate functional data analysis for fast uncertainty quantification in subsurface reservoir forecasting

Wednesday, 17 December 2014
Ognjen Grujic, Stanford University, Stanford, CA, United States and Jef Caers, Stanford Earth Sciences, Stanford, CA, United States
Modern approaches to uncertainty quantification in the subsurface rely on complex procedures of geological modeling combined with numerical simulation of flow & transport. This approach requires long computational times rendering any full Monte Carlo simulation infeasible, in particular solving the flow & transport problem takes hours of computing time in real field problems. This motivated the development of model selection methods aiming to identify a small subset of models that capture important statistics of a larger ensemble of geological model realization. A recent method, based on model selection in metric space, termed distance-kernel method (DKM) allows selecting representative models though kernel k-medoid clustering. The distance defining the metric space is usually based on some approximate flow model. However, the output of an approximate flow model can be multi-variate (reporting heads/pressures, saturation, rates). In addition, the modeler may have information from several other approximate models (e.g. upscaled models) or summary statistical information about geological heterogeneity that could allow for a more accurate selection. In an effort to perform model selection based on multivariate attributes, we rely on functional data analysis which allows for an exploitation of covariances between time-varying multivariate numerical simulation output. Based on mixed functional principal component analysis, we construct a lower dimensional space in which kernel k-medoid clustering is used for model selection. In this work we demonstrate the functional approach on a complex compositional flow problem where the geological uncertainty consists of channels with uncertain spatial distribution of facies, proportions, orientations and geometries. We illustrate that using multivariate attributes and multiple approximate models provides accuracy improvement over using a single attribute.